The Big Bang Model and the Cosmological Principle

In spite of the foregoing difficulties it might still be argued
that Big Bang model must be correct because it predicts a universe
in accord with the Cosmological Principle, viz., that the universe
appears the same irrespective of the location of the observer
in the universe. The problem with this argument is that we really
do not know the Cosmological Principle is true. In fact, all
that we know is that the large scale structure of the universe
appears to be approximately isotropic (i.e., the same in all
directions) from our present point of observation. Modern cosmology
justifies the Cosmological Principle by coupling the observation
of isotropy about our position with the assumption that our galaxy
does not occupy a special position in the universe. That is,
if our galaxy occupies a non-specific or arbitrary position in
the universe, then it follows the universe must be isotropic
everywhere and hence homogeneous as well.

But what if our galaxy does occupy a privileged position in
the universe? First, it would no longer be logical to extrapolate
the isotropy which we observe to the other parts of the universe,
which means it would no longer be possible to justify either
the condition of homogeneity or the cosmological principle. Second,
the simplest deduction of the observed isotropy of the universe
from our location is that the universe must be spherically symmetric
about either the Milky Way or some point which is astronomically
nearby. But spherical symmetry about any point in the universe
implies that point is the Center, and this brings us to the discussion
of the creation model.

A Creation Model of the Universe: The Fundamental Postulate

The fundamental premise of the Judeo-Christian creation model
of the universe is determined by the scripture, "The Lord has
established His throne in the heavens, and His kingdom ruleth
over all." Psalm 103:19 (RSV). On the basis of this statement
it is evident that the Creator has established, or fixed, His
throne at some point in the universe, which in my view is none
other than the Center of the universe. It is axiomatic that a
fixed point in the universe requires the existence of a fixed
or absolute reference frame. Previously [p. 287] it was noted that the
CMR has been recognized as establishing an absolute reference
frame (45); so it is quite clear that the fundamental postulate
of this creation model of the universe is based on tangible scientific
evidence.

The Revolving Steady State Model of the Universe: A Brief
Description

Assuming there is a Center (C) to the universe, I propose
that the galaxies are not receding from each other as presently
supposed, but instead are revolving at different distances and
at different tangential speeds around C. On this basis all galaxies
must have a tangential velocity around C. Measurements have shown
that our solar system, and hence the Milky Way, has a cosmic
velocity through the CMR (46), and it is this velocity which
is identified with the tangential velocity of the Milky Way around
C. In this view C must lie somewhere in that plane which passes
through the MW which is also perpendicular to the cosmic velocity
vector of the MW. It is evident that the RSS model pictures the
galaxies orbiting C in any one of many different-sized concentric
shells which suggests the alternate designation 'Shell Model
of the Universe.'

As originally conceived this Revolving Steady State (RSS)
model envisions a universe with galaxies which move in circular
orbits under the gravitational field produced by all of them.
The field is assumed to be stationary and spherically symmetric.
Decades ago Einstein made a general relativity study (47) of
circulating particles constrained by this type of gravitational
field, but his analysis did not mention redshifts, nor was there
any hint that he considered his analysis had any reference to
the structure of the universe.

The RSS Model and Galactic Redshifts

Assuming the galaxies are revolving in different orbital planes
and with different tangential velocities v around some universal
center C, initially I thought that if the Milky Way was one of
the innermost galaxies, then most of the galactic redshifts as
observed on earth might be due to a combination of gravitational
and transverse Doppler effects. (A literature search showed that
Burcev (48) had proposed over a decade ago that quasars were
possibly stellar objects whose redshifts might be attributable
to the transverse Doppler effect.)

Although questions have arisen about this explanation for
the galactic redshifts in the RSS model, it seems worthwhile
to explain my original rationale and the objections which now
appear to present themselves. In particular, in the Newtonian-based
RSS model the galaxies of mass m and tangential velocity v remain
in circular orbits by gravitational attraction of the total mass
M within the sphere of orbital radius R. In this scenario, mv2/R
= mMG/R2, or v2 = GM/R, where G is the
gravitational constant. Thus an observer on an innermost galaxy
located at a distance R1 from C would in theory see
light from a more distant galaxy (at R2 from C) shifted
in frequency because of the transverse Doppler effect and the
change in gravitational potential V(R) = −GM/R. The presumed
limiting distance R' at which galaxies could remain in stable
orbits would be when the tangential velocity v = c, the velocity
of light. Beyond this presumed galactic cutoff distance the RSS
model tentatively assumes a rapidly diminishing mass/energy density
so that we do not encounter an infinite gravitational potential
(see discussion of equations (2) and (3) for more details).

The frequency shifts expected in the RSS model can be compared
to an earth-bound [p. 288] observer comparing the frequency of a light
signal emitted from his position on the rotating earth's surface,
where the tangential velocity is v1, and the gravitational
is V1, with the frequency of the same signal emitted
from an overhead satellite which is orbiting with velocity
v2 in a gravitational potential V2. The
experimentally confirmed (41) equation for the redshift, as derived
from the principle of equivalence, is:

(1)

z = (V1 − V2) / c2 − (v12 − v22) / 2c2.

The same equation applies in the RSS model except that v1
and V1 are the cosmic velocity and gravitational potential
of the Milky Way at R1 from C whereas v2
and V2 represent the same quantities for a more distant
galaxy at R2 from C.

Another source of frequency shifts arises because the Milky
Way (MW) is not exactly at C. In this case the more distant galaxies,
which are rotating away from or toward the MW, produce first
order Doppler redshifts or blueshifts. The blueshifts, which
would be most pronounced for nearby galaxies, can be eliminated
for all practical purposes if it is assumed that the more distant
galaxies are rotating away from the MW. This scenario would result
in a recessional redshift which, because it depends on the cosine
of the angle between the velocity vector of the outer galaxy
and the line of sight from the MW to that galaxy, would diminish
with distance. Thus, of itself this redshift could at most be
only a part of the total galactic redshift observed on the earth.
Of course, a significant distance-related redshift, irrespective
of its origin, could overshadow most blueshifts expected from
galaxies rotating toward the MW and eliminate the need for assuming
rotation away from the MW.

We now return to the discussion of the redshifts expected
on the basis of eq. (1). If the ρ,
the mass/energy density of the universe is assumed to be constant
then M = 4 πρ R3/3,
and substitution of the appropriate quantities into eq. (1) leads
to the formal result that z is proportional to R2,
which is of the same form of the redshift relation proposed
in references (33,34,37-39).
On a similar basis, if the density
is assumed to vary inversely as R, then one can obtain an expression
for z which is proportional to R, which is of the same form as
the Hubble relation (49).

Of course, astronomers measure apparent magnitudes, not distances,
and, for there to be a quantitative comparison between the above
results and the redshift distribution, the light flux relation
for the RSS model must be formulated so as to include the combined
effect of the redshift and gravitational focusing. This formulation
has yet to be done; thus on this basis alone it would be premature
to claim the forgoing results are consistent with the galactic
redshift relation proposed by Nicoll and Segal (38). Moreover
it should be remembered that if the universe is revolving, then
an extraneous factor has been included into the data which comprise
the redshift distribution, and this would preclude any immediate
comparison. But regardless of the outcome of the above calculations,
there seems to be a more fundamental objection to the preceding
formulation.

In particular, we must carefully investigate whether the gravitational
potential V = −GM/R used in the above calculations is the correct
expression for the potential function. It is of crucial importance
to know whether it is correct for it is used as the basis for
the derivation of the Hubble relation (31,32) in Big Bang cosmology.
According to Silk (31) and Weinberg (32), its use in computing
the potential at the surface of an arbitrarily large, but finite
sphere, of radius R within an infinite universe is justified
by a theorem [p. 289] due to Birkhoff. Part of the proof of this theorem
implicitly assumes that the universe is structured according
to the Cosmological Principle. Now the creation model of the
universe proposed herein is also of infinite extent, but the
Cosmological Principle does not hold, so that there is no basic
reason why this theorem should yield the correct gravitational
potential in the RSS model. But should it hold for the Big Bang
model?

To answer this question we first note that the negative gradient
of the potential V = −GM/R yields a repulsive force per unit
mass F/m = GM/R2 whereas there is an experimentally
confirmed theorem in classical mechanics which definitely requires
an attractive force per unit mass F/m = −GM/R2 to
exist at any point R within a sphere enclosing a uniform mass
distribution. This latter result is an integral part of both
the RSS and the Big Bang models. Thus the potential V = −GM/R
is just as wrong for the Big Bang model as it would be for the
RSS model because it yields an incorrect sign for the force.
Even Silk's (31) elementary treatment (see page 332) makes it
clear that the derivation of the Friedmann equation for the Big
Bang expanding universe is based on the potential V = −GM/R.
Here we have a logical contradiction in the theoretical development
of the primeval fireball, which is of course the basis for predicting
the Hubble relation in the Big Bang.

An expression for the potential (50,51)
which does yield the correct attractive force is given by

(2)

V(R) = −GM/R− G ∫R∞ 4 πρ r drwhere M = 4π ∫oR ρr2dr.

The problem here is that for a finite, uniform density we
encounter an infinite potential due to the presumed infinite
size of the universe. This result is the same for both the Big
Bang model and the RSS model.

Alternatively, a finite potential can be obtained from eq.
(2) by assuming the density diminishes more rapidly than 1/R3
after R', where v = c. As a first approximation this assumption
truncates the potential at R'. In this case the upper integration
limits in eq. (2) must be changed from infinity to R', and we
have the following potential:

(3)

V(R) = −GM/R− G ∫RR' 4 πρ r drwhere M is defined in eq. (2).

If this potential is used in eq. (1) to compute z for
the RSS model, then for a uniform density for all R less than
R', we find the redshift is zero. If, however, the density increases
as R0.22 then we can formally obtain a relation (51)
similar to that deduced by Hawkins (34). Again, however, it is
premature to make any claims about this result until more work
is done.

Another possibility for obtaining redshifts in the RSS model
is to assume the mass/energy density diminishes as 1/R4.
In this case the galactic orbits are no longer circular but
spirals, and there is a recessional component to the velocity
which leads to a first order Doppler shift and a Hubble type
z ∝ R relation. For this view to
have any credibility most of the mass/energy of the universe
must be in a form other than the matter and radiation energy
presently observed and/or inferred in stellar systems and intergalactic
dust. In this context it is perhaps worth mentioning that Ellis
(52) has proposed that there may be a large amount of undetected
mass/energy in other forms (e.g., neutrinos) which could raise
the cosmic mass/energy density to more than a million times the
present density estimates of 10−31to 10−29g/cm3.

[p. 290]

Of course the RSS model does not require that the redshifts
are velocity dependent. In this respect it is well known that
years ago proponents of a static or steady state universe proposed
a variety of distance-dependent interpretations of the redshift
which were non-recessional in nature (see North's (42) review
for details and references). The investigation of the origin
of the redshifts in the RSS model should include a reexamination
of these alternatives.